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Circulation of a stream function

  1. Sep 14, 2010 #1
    1. The problem statement, all variables and given/known data
    The stream function of a 2D incompressible flow is given by:

    [tex]\Psi[/tex]=([tex]\Gamma[/tex]/2pi)*ln(r)

    Show that the circulation about a closed path about the origin is [tex]\Gamma[/tex] and is independent of r.

    2. Relevant equations

    [tex]\Gamma[/tex]=-[tex]\oint[/tex]V dot ds

    3. The attempt at a solution

    So far I know that the radial velocity component Ur=(1/r)*d(Psi)/d(theta)=0 because Psi does not depend on theta.
    This means that the angular velocity component is the only velocity component: Utheta=-d(Psi)/d(r)=-L/2pi(r)
    After this point im not exactly sure what to do.
     
    Last edited: Sep 14, 2010
  2. jcsd
  3. Sep 14, 2010 #2
    Cant really understand the latex stuff... working on it
     
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